FOURTH EDITION

_PRICE TWO SHILLINGS_

London
MACMILLAN AND CO., LIMITED
NEW YORK: THE MACMILLAN COMPANY
1897

_All rights reserved_

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RICHARD CLAY AND SONS, LIMITED,
LONDON AND BUNGAY

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ADVERTISEMENT.

An envelope, containing two blank Diagrams (Biliteral and Triliteral)
and 9 counters (4 Red and 5 Grey), may be had, from Messrs. Macmillan,
for 3_d._, by post 4_d._

* * * * *

I shall be grateful to any Reader of this book who will point out any
mistakes or misprints he may happen to notice in it, or any passage
which he thinks is not clearly expressed.

* * * * *

I have a quantity of MS. in hand for Parts II and III, and hope to be
able----should life, and health, and opportunity, be granted to me, to
publish them in the course of the next few years. Their contents will be
as follows:--

_PART II. ADVANCED._

Further investigations in the subjects of Part I. Propositions of other
forms (such as "Not-all x are y"). Triliteral and Multiliteral
Propositions (such as "All abc are de"). Hypotheticals. Dilemmas. &c.
&c.

_Part III. TRANSCENDENTAL._

Analysis of a Proposition into its Elements. Numerical and Geometrical
Problems. The Theory of Inference. The Construction of Problems. And
many other _Curiosa Logica_.

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PREFACE TO THE FOURTH EDITION.

The chief alterations, since the First Edition, have been made in the
Chapter on 'Classification' (pp. 2, 3) and the Book on 'Propositions'
(pp. 10 to 19). The chief additions have been the questions on words and
phrases, added to the Examination-Papers at p. 94, and the Notes
inserted at pp. 164, 194.

In Book I, Chapter II, I have adopted a new definition of
'Classification', which enables me to regard the whole Universe as a
'Class,' and thus to dispense with the very awkward phrase 'a Set of
Things.'

In the Chapter on 'Propositions of Existence' I have adopted a new
'normal form,' in which the Class, whose existence is affirmed or
den